In the fall of 1986, the authors developed a prototype of a fast GF(2593) multiplier/exponentiator. This device was based on the discovery of optimal normal basis structures in fields of characteristic two [1][2]. In the ensuing years, much effort has gone into fabricating this structure as a VLSI device. In the early months of 1989, the first functioning VLSI devices were fabricated [3]. These devices, which implement a cryptographic system based on discrete exponentiation [4][5], have throughput rates of up to 300 Kbps.. Many cryptographic applications based on discrete exponentiation have been implemented or proposed [6][7], and several new applications of the normal basis multiplier have recently been considered.
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